The chain keeps making loud cracking noises and jumps off frequently. I've checked chainline (meticulously) and thats ok, the chain is tight enough (tightened it right up in frustration but still happens).

I can't understand why its doing this, never had a problem before, and only teh chain is a not-tried-before item. Unfortunately last night, on the last road climb home, it skipped off as I was standing up stamping on the pedals, depositing me chin-first into the tarmac. Cue holes in chin and knee, golf ball bruise on thigh and very sore ribs. So got to get this fixed.

Yep - try a different chain. I had a similar mysterious issue with a Wipperman chain once. Just wasn't happy in the ring/freewheel combo I had (MTB ss). Same chain was fine on another set up (road fixie) when I sued it a few months later.

iiiiiinteresting. I just recently installed a new on one 34 ring, ss 17t sprocket. First off a nearly new 9 speed chain - and within a couple of pedal revolutions it was not right.

So replaced with brand new PC1... and exactly the same thing. Chainline wasn't perfect so I tweaked that and the tensioner. It now seems perfect on the stand but yet to actually ride it (this afternoon's ride!).

fwiw I have a wide bas ssc sprocket and it is that which is a little bit eggshaped (ring is pretty round and was great with old smaler sprocket): shame really as other wise I would try and put the 'eggs' at right angles to each other to see if it cancels out..) I don't get jumpy-chain on climbs, but it does make worrying creaky cracky noises under heavy load/gurn, and it is hard to get the tension 'just so' if you want longish freehub life and you don't want it rattling off over roots and jumps.

OP, sounds like you know what the chainline should look like, only other thing I would check before an 8-speed (ie narrower) chain is that the teeth on chainring and sprocket are all nice and straight and free of burrs etc. Unlikely as they are new, but I have experienced this (with 1mm of bent tip on a tooth on a ramped chainrings on a geary bike) which only reared its head when the chain was under heavy load.

Thought mine was egged too, but just rode it anyway until it wore out. Now swapped for a surly one. That must be egged too! Or my chainring isn't centred. Anyway - not an issue with either sprocket once I swapped to kmc 3/32" chains.

Also looking at how much 'wobble' my freehub has, i'm not going to worry about a small amount of egging or a non-centred chainring.

Spooky, I've got a very similar problem but on my Rohloff set up. 1 x new 16t sprocket and 1 x new izumi track chain. I think the common denominator may be the 1/8" chain on a 3/32" sprocket. I've tightened mine right up and will be heading out for a spin tomorrow AM so if that doesn't work, it'll get binned and swapped for a 3/32" chain.

Try wrapping the chain around the entire cog, both front and rear cogs individually. If it's the right size chain then it will map against the cogs perfectly. Hold the chain tight (obviously easier to do with the parts off the bike) and see if there's any raised spots. Any thing raised in then chain indicates that the teeth are not compatible with your chain dimension.

Some chains are direction specific, though i suspect that only effects shifting, with the text (manu logo) to be send from the outside of the bike.

Re-tight spots, find the tightest part of the chain, slacken off your front ring bolt s a little and then tap the chain (in the tightest spot) with a big screwdriver handle. Re-tighten your bolts individually but opposite to one another a little each at a time.

also - do you know how to calculate your chain line correctly. Don't go by eye, you ideally need callipers to get an accurate measurement.

40mpg you mentioned tight and loose spots. When you're grunting on the pedals frame flex will cause loose spots to become very loose spots. Maybe try a narrower chain that will be held straighter by the teeth on the sprockets. 1/8 chain really needs wider BMX type sprockets to work properly.

Yep sounds like the chain is too wide. I had a repair in the other day and the same was happening. Pedalling it slowly in the workstand you could see the chain riding over to one side of the rear sprocket, then an inner link would catch a tooth and try and jump off. Fitted a 3/32 and it worked fine.

The superstar are 3/32 as I guess is the chain ring. Try to use all same, mines all 1 1/8. I use halo fat foot cog and velosolo single speed alloy chain ring with any 1 1/8 chain. Never had a single problem and very strong.

You don't need quite a bit of slack - if you can spin the cranks backwards by hand freely then it's not too tight.
Those Superstar sprockets don't have as good a tooth profile as, say, Surly or Chris King - plus check for a bent tooth on either the sprocket or chainring. Use a KMC Z610HX chain, probably about the best there is, in my opinion.
I can honestly say that during the time that I've been riding singlespeeds I've never had any drivetrain problems - Surly or CK sprockets, KMC chain and Middleburn Uno ( or HBC) chainrings.
I'm not ultra fastidious about chain line or tension either - I just set the chain line by eye and have as little chain slack as possible without any feeling of binding..